Can I filter barking sounds on the television?
OK, here is one approach. 


Acquire a data set of 'clean' audio samples without barking dogs and an data set of barking dogs sounds.
Generate a training set by mixing random selections of clean audio with a random selections of barking dog noises at various volume levels. This is your input data. Your output data is the clean audio before you added the barking.
Find a suitable neural network. This might be a good starting point: https://github.com/andabi/music-source-separation
Train the network.
Apply the network to a load of the clean+bark mixes and check the result by ear. If the results are not good enough, go to 3 to tweak the network. If the results are still poor go to 2 and generate more training data, perhaps adding some distortions or other effects the the barking. Happy with the result? Go to 6.
Publish the results online for the betterment of humanity. (And/or write the network to  a miniature GPU board (such as the NVIDIA Jetson https://developer.nvidia.com/buy-jetson) and work out how to wire that up to the decoded audio in your telly before it heads to the speakers), then blog about it because that would be a great project.